Holographic Wilson loops

Abstract

In its simplest version, the Anti-de Sitter (AdS)/Conformal Field Theory (CFT) correspondence maps non-perturbative questions in gauge theory dynamics to problems in classical gravity. One of our goals is to understand how the correspondence works beyond this "large N" approximation. The holographic description of Wilson loops plays a salient role in this task due to the existence of exact results on the field theory side of the conjecture. We are interested in semi-classically studying string and D-brane configurations dual to Wilson loop operators and matching this analysis with gauge theory predictions. Along the way, this should lead us to new exciting challenges in the field of holography.Wilson loops (WL) are an important class of gauge invariant non-local operators. In the case of N = 4 super Yang-Mills theory, the AdS/CFT correspondence states that half BPS operators in the fundamental representation of SU(N) have a dual description in terms of a string with an AdS2 worldsheet. To capture more general representations one must consider instead D3 or D5 branes with worldvolume flux. In these cases, the classical supersymmetric solutions correspond to AdS2 × S2 and AdS2 × S4.A natural step is to seek a semi-classical understanding of the string and D-brane solutions dual to WL operators. In a series of papers, A. Faraggi and collaborators found the spectrum of excitations of the D3 and D5-brane configurations. By studying both bosonic and fermionic fluctuations exhaustively, we were able to show that the spectra fit nicely into short multiplets of OSp(4|4). Furthermore, the one-loop effective action for the D5 brane was computed.This line of inquiry opens the possibility of performing precision tests of AdS/CFT. On the one hand, we can compute the one-loop functional determinants due to the brane fluctuations. On the other, as argued in the seminal work of Erickson-Semenoff-Zarembo and Drukker-Gross, the circular WL is described exactly by a Gaussian matrix model and can be solved perturbatively order by order. Comparing the two results would shed light on how the correspondence acts beyond the leading order in 1/N. It is also an intriguing possibility that AdS/CFT can tell us something about the quantum theory of extended objects.Our research proposal entails carrying out this program in full detail. In particular, we are interested in computing the functional determinants due to the D3-brane fluctuations which has not been done yet. We would also like to revisit the case of the fundamental string where partial results seem to disagree with the prediction of the matrix model. It is worth mentioning that, because the geometries involved posses and AdS2 factor, this problem bears some similarity to that of computing corrections to extremal black hole entropy. The plan also includes addressing issues about holographic renormalization on D-branes, more general D-brane fluctuations, and condensed matter applications. At the same time, we would like to expand our efforts to other areas such as black hole thermodynamics and higher spin gravity, which have received considerable attention in the community. (AU)